Mark Hamill was born September 25, 1951 and is an American stage, screen and voice actor. He is best known as Luke Skywalker of the "Star Wars" franchise and as the voice of "the Joker in the "Batman: The Animated Series" and follow-on shows. He is also among the unique set of actors who have portrayed a version of themselves on "The Big Bang Theory".
In "The Bow Tie Asymmetry", Howard found his dog Bark Hamill. Mark offers Howard a reward followed by a favor. Howard gets him to perform the Shamy wedding as a surprise to Sheldon displacing Wil Wheaton. Before performing the ceremony, he fills in time taking Star Wars questions that he can't answer; however, Stuart can answer them. Mark also breaks down during the ceremony because he thinks the vows are so beautiful.
In the episode, Mark Hamill apparently does not know who Wil Wheaton is, but in real life they are very familiar with each other.